On Jul 17, 5:01=A0pm, "stefanba...@[EMAIL PROTECTED]
" <stefanba...@[EMAIL PROTECTED]
>
wrote:
> On Jul 17, 1:01 pm, "Science.Medical.Imaging List"
>
>
>
>
>
> <pixel.to.l...@[EMAIL PROTECTED]
> wrote:
> > On Jul 17, 12:05 pm, "stefanba...@[EMAIL PROTECTED]
" <stefanba...@[EMAIL PROTECTED]
>
> > wrote:
>
> > > On Jul 17, 11:57 am, "stefanba...@[EMAIL PROTECTED]
" <stefanba...@[EMAIL PROTECTED]
>
> > > wrote:
>
> > > > On Jul 16, 9:14 am, "Science.Medical.Imaging List"
>
> > > > <pixel.to.l...@[EMAIL PROTECTED]
> wrote:
> > > > > On Jul 16, 1:37 am, Mauro <mauro.ita...@[EMAIL PROTECTED]
> wrote:
>
> > > > > > Hi all,
> > > > > > I would like to understand better the idea of frequency (in
the
> > > > > > spatial domain) of an image in relation with an imaged object.
=
Is the
> > > > > > frequency measured in pixels/cm or cm/pixels?
> > > > > > Mainly becuase I would like to see whether the Nyquist
frequenc=
y is
> > > > > > satisfied over an imaged object in a 3d volume (CT).
>
> > > > > > thanks,
> > > > > > Mauro
>
> > > > > Mauro,
>
> > > > > There can be several ways of estimating the frequency of a
signal=
..
> > > > > Take a simple case of a 1 dimensional signal, a finite ****tion
of
> > > > > which has been digitized (sampled along equal intervals using
som=
e
> > > > > spread function). Also, lets assume you know that width of the
fi=
nite
> > > > > ****tion in some spatial units, lets say cm.
>
> > > > > In this case, then, the frequency of the signal as estimated in
t=
he
> > > > > digitized spatial domain will be: (number of pixels in digitized
> > > > > signal / length in cm of the signal ****tion).
>
> > > > > Meaning, higher the number of pixels in the 1D image, the finer
y=
ou
> > > > > sampled over the original signal =3D> higher frequency.
>
> > > > > To ensure your sampling method is using at least a Nyquist
freque=
ncy
> > > > > or higher, you will first need to know the frequency of the
origi=
nal
> > > > > signal. Then you will nede to make sure you sample it enough
time=
s
> > > > > (enough pixels) that will capture even the finest detail in the
s=
ignal
> > > > > that would occur in the smalles relative spatial region.
>
> > > > It is not so straightforward. It is correct only for
Classification
> > > > Interpolation (CI) and if lighting does not use scalar field
> > > > gradients. It is plainly wrong for IC and lighting with original
> > > > gradients.
>
> > > One correction: my statement above is an accurate if assume that
> > > =93original signal=94 means the density-scalar field before
digitizin=
g; CT
> > > data is one of such examples of digitized scalar field.
>
> > > > > For a 3D CT case, I assume you are talking about resampling an
al=
ready
> > > > > digitized image data. Is that correct? If so, you will need to
fi=
nd
> > > > > out the highest frequency of a feature that you dont want to
lose=
in
> > > > > the image after resampling. If the image is not isotropic (has
> > > > > different frequency along three dimensions), you will need to
rep=
eat
> > > > > this for all three directions and get the highest frequency of
al=
l for
> > > > > simplicity. Then you will need to make sure the frequency of the
> > > > > resampling kernel is higher than the Nyquist rate, given the
high=
est
> > > > > frequency.
>
> > > > > Hope this helps.
>
> > > > >
[http://groups.google.com/group/medicalimagingscience/web/smiview=
er-
> > > > > download-page]- Hide quoted text -
>
> > > - Show quoted text -- Hide quoted text -
>
> > > - Show quoted text -
>
> > What you say is a special case where one would want to estimate
> > optical properties from image information, with an additional
> > assumption that the image data, in some form, depicts the density of
> > the material imaged =A0(for direct volume rendering of CT data for
> > example).
>
> > The original post does not say anything about rendering, hence my
> > reply was very general, focussed only on resampling of an already
> > digitized signal.
>
> > Your point taken, however, for the special case in VR where you would
> > want to interpolate first then classify.
>
> > Anyways, its just a matter of what you treat as 'original' data, and
> > how you measure the accuracy of resampling. The basic concept behind
> > 'sample a signal enough to retain high frequency features' remains the
> > same.. theres nothing more to it. Its up to us if/how we have to
> > complicate its interpretation based on our needs.
>
> SMI> The basic concept behind 'sample a signal enough
> SMI> to retain high frequency features' remains the
> SMI> same.. theres nothing more to it.
>
> Apparently you are right but it is the rightness of sampling theorem.
> I do not think the poster was looking for so rudimentary basic stuff,
> may be I=92m wrong about it though.- Hide quoted text -
>
> - Show quoted text -
Thank you for the clarification. It never hurts to discuss a question
like this: we get to see so many different perspectives to a problem.
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